Infestation Terminus
Target 1 "lswarm" monster you control and 2 cards your opponent controls; banish the first target, and if you do, Return the second targets to the hand.

Quote:

Evilswarm Thunderbird
During either player's turn, when a card or effect is activated (except during the Damage Step): You can banish this card you control. During your next Standby Phase, Return this card banished by this effect to the field, and if you do, it gains 300 ATK. You can only use the effect of "Evilswarm Thunderbird" once per turn.

Question:
Can Evilswarm Thunderbird chain to evade itself from banishing effect of Infestation Terminus?
My cousin insisted that he can chain Evilswarm Thunderbird to prevent it from banishing while two of my monsters will Return in hand, and his Evilswarm Thunderbird can Return during the stand by phase.

Same as:

Quote:

Infestation Infection
Once per turn: You can shuffle 1 "lswarm" monster from your hand or face-up on your field into the Deck; add 1 "lswarm" monster from your Deck to your hand.

He activated Infestation Infection returning Evilswarm Thunderbird to hand, and then chained it to prevent it from returning and then he adds 1 "lswarm" monster from his deck.

His primary argument is that, Infestation Terminus/Infestation Infection is not a COST, it is part of the effect so he can chain Evilswarm Thunderbird any time he wants.

Note the "and if you do" in Terminus' text. This means that if the first part does not happen (in this case, the banishing of Thunderbird by Terminus, not by Thunderbird itself), then anything afterward does not happen either.
He can chain it if he wants, but nothing will happen.

With Infection, the returning to the Deck is a cost as the semicolon following the initial text denotes.